This paper proposes a discrete-time adaptive control approach for uncertain single-input and single-output (SISO) linear time-invariant sampled-data systems with uncertain, constant input time delay that has a known upper-bound, without explicitly estimating the time delay. To cope with the unknown time delay a reduction approach similar to that proposed by Artstein in 1982 is used which results in a delay-free system that simplifies the control law design. In addition, the proposed control approach is capable of coping with bounded exogenous disturbances. A rigorous stability analysis shows that the proposed control approach drives the system output to a bound around the reference signal asymptotically, in the presence of an exogenous disturbance. Moreover, simulation results are shown to verify the approach.
This paper proposes a discrete-time adaptive regulation approach for scalar linear time-invariant systems with unknown, constant input time delay that has a known upper-bound, without explicitly estimating the time delay. To cope with the unknown time delay, a state substitution is made that results in a delay free system that simplifies the control law design. In addition, the proposed approach does not require that the system have stable open-loop zeros. A stability analysis shows that the proposed regulator drives the system state to zero asymptotically and simulation results are shown to verify the approach.
This paper presents an approach for developing a neural network inverse model of a piezoelectric positioning stage, which exhibits rate-dependent, asymmetric hysteresis. It is shown that using both the velocity and the acceleration as inputs results in overfitting. To overcome this, a rough analytical model of the actuator is derived and by measuring its response to excitation, the velocity signal is identified as the dominant variable. By setting the input space of the neural network to only the dominant variable, an inverse model with good predictive ability is obtained. Training of the network is accomplished using the Levenberg-Marquardt algorithm. Finally, the effectiveness of the proposed approach is experimentally demonstrated.
A discrete-time adaptive regulator for uncertain MIMO LTI systems with input delays is proposed. The input delays are assumed to be constant and unknown except for a known upper bound, and it is possible for delays to be different across input channels. An adaptive estimator is used for online parameter estimation, and the control law is obtained by applying Artstein's model reduction to the adaptive model after is has been rewritten using second order difference. The resulting controller is, then, able to stabilize the system while mitigating the effects of the unmeasurable exogeneous disturbances.
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